(x-2y)*(x-5y)=

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Solution for (x-2y)*(x-5y)= equation: 


Simplifying
(x + -2y)(x + -5y) = 0

Multiply (x + -2y) * (x + -5y)
(x(x + -5y) + -2y * (x + -5y)) = 0
((x * x + -5y * x) + -2y * (x + -5y)) = 0

Reorder the terms:
((-5xy + x2) + -2y * (x + -5y)) = 0
((-5xy + x2) + -2y * (x + -5y)) = 0
(-5xy + x2 + (x * -2y + -5y * -2y)) = 0
(-5xy + x2 + (-2xy + 10y2)) = 0

Reorder the terms:
(-5xy + -2xy + x2 + 10y2) = 0

Combine like terms: -5xy + -2xy = -7xy
(-7xy + x2 + 10y2) = 0

Solving
-7xy + x2 + 10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y)(x + -2y) = 0


Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve:

Simplifying
x + -5y = 0

Solving
x + -5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '5y' to each side of the equation.
x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
x + 0 = 0 + 5y
x = 0 + 5y
Remove the zero:
x = 5y

Simplifying
x = 5y

Subproblem 2
Set the factor '(x + -2y)' equal to zero and attempt to solve:

Simplifying
x + -2y = 0

Solving
x + -2y = 0

Move all terms containing x to the left, all other terms to the right.

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y
Solution
x = {5y, 2y}

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